Definition 1.6 (\(A_p\)  weights class,[1]},[2]}) 
Let \(p\in [1,\,\infty )\)  and \(w\)  be a nonnegative, locally integrable function on \(\mathbb {R}^d\) . We say that \(w\in A_{p}(\mathbb {R}^d)\)  if the \(A_p\)  constant \([w]_{A_p}\)  is finite, where
\([w]_{A_p}:=\sup _{Q}\Big (\frac{1}{|Q|}\int _Qw(x)dx\Big )\Big (\frac{1}{|Q|}\int _{Q}w^{-\frac{1}{p-1}}(x)dx\Big )^{p-1},\,\,\,p\in (1,\,\infty ),\) 
